This is the second of series of papers studyig moduli spaces of a certain class of coherent sheaves, which we call stable perverse coherent sheaves, on the blow-up p : X̂ → X of a projective surface X at a point 0. The followings are main results of this paper: a) We describe the wall-crossing between moduli spaces caused by twisting of the line bundle O(C) associated with the exceptional diviso...

This article introduces a universal moduli space for the set whose archetypal element is a pair that consists of a metric and second fundamental form from a compact, oriented, positive genus minimal surface in some hyperbolic 3–manifold. This moduli space is a smooth, finite dimensional manifold with canonical maps to both the cotangent bundle of the Teichmüller space and the space of SO3(C) re...

Gelfand’s [1] charecterization of a topological space M by the duality relationship of M and A = F(M), the commutative algebra of functions on this space has deep implications including the development of spectral calculas by Connes [2].We investigate this scheme in this paper in the context of Monopole Moduli Space M using Seiberg-Witten Equations [3].A observation has been made here that the ...

This is the second of our two papers on the Siegel-Weil theorem for loop groups. In the first paper [3] we proved the Siegel-Weil theorem for (finite dimensional) snt-modules ([3], Theorem 8.1). In the present paper we use this result to obtain the Siegel-Weil theorem for loop groups, Theorem 7.5, below. In addition to the corresponding result for snt-modules, our proof depends on a convergence...

For a compact, connected Lie group G, we study the moduli of pairs (Σ,E), where Σ is a genus g Riemann surface and E →Σ is a flat G-bundle. Varying both the Riemann surface Σ and the flat bundle leads to a moduli space Mg , parametrizing families Riemann surfaces with flat G-bundles. We show that there is a stable range in which the homology of Mg is independent of g. The stable range depends o...

We know that there is an isomorphism between the moduli space of gauge equivalence classes of flat G-connections on a compact surface and the moduli space of representations from the fundamental group of the surface to G acted on by the adjoint action (cf: Goldman[G]). It is known that if G is compact, semi-simple and simply connected, the moduli space of gauge equivalence classes of flat G-con...

A moduli problem in algebraic geometry is the problem of constructing a space parametrizing all objects of some kind modulo some equivalence. If the equivalence is anything but equality, one usually has to impose some sort of stability condition on the objects represented. In many cases, however, this stability condition is not canonical, but depends on a parameter, which typically varies in a ...

In this paper we study two different topics. The first topic is the applications of the geometric quantization scheme of Witten introduced in [2] and [16] to the problem of the quantum background independence in string theory. The second topic is the introduction of a Z structure on the tangent space of the moduli space of polarized CY threefolds M(M). Based on the existence of a Z structure on...

We study the phase structure of four-dimensional N = 1 super Yang-Mills theories realized on D6-branes wrapping the RP of a Z2 orbifold of the deformed conifold. The non-trivial fundamental group of RP allows for the gauge group to be broken to various product groups by Z2 Wilson lines. We study the classical moduli space of theories in various pictures related by dualities including an M-theor...